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Topic: A New Graph Coloring Conjecture.
Replies: 42   Last Post: Jul 2, 2013 4:08 AM

 Messages: [ Previous | Next ]
 b92057@yahoo.com Posts: 1,187 Registered: 4/18/05
Re: A New Graph Coloring Conjecture.
Posted: Jul 1, 2013 7:23 PM

On Saturday, June 29, 2013 12:06:44 AM UTC-7, quasi wrote:
> >quasi wrote:
>
> >> bill wrote:
>
> >> >quasi wrote:
>
> >> >> bill wrote:
>
> >> >> >
>
> >> >> >Forced Five Set: A connected subset of five vertices
>
> >> >> >(not isomorphic to K5), that cannot be 4-colored.
>
> >> >>
>
> >> >> With the definition as you've stated it, there's no such
>
> >> >> thing as a forced 5-set.
>
> >> >
>
> >> >Am I the only person who would like to see a short
>
> >> >snappy proof of the 4 CT?
>
> >>
>
> >> Sure, that would be nice.
>
> >>
>
> >> >I hope to create a simple proof of the Four Color Theorem.
>
> >> >In this context, I don't think that I will be allowed to
>
> >> >presume that forced sets do not exist.
>
> >>
>
> >> But you _will_ be expected to give a rigorous mathematical
>
> >> definition of forced sets. You previously said you couldn't
>
> >> do that.
>
> >
>
> >Give me the mathematical definition of an impasse and
>
> >I will try to adopt it to include forced sets.
>
> >> >
>
> >> >I m fairly certain that a forced set may be cited as
>
> >> >the primary reason for the more common impasses.
>
> >> >
>
> >> >In this context; an unresolved impasse in the attempted
>
> >> >4-coloring of a planar graph might be due to the presence
>
> >> >of a forced set.
>
> >>
>
> >> If you can't define forced sets in a way that others can
>
> >> understand, there's not much chance that anyone would be
>
> >> able to follow a proposed proof of yours of the 4CT.
>
> >
>
> >Can you accept this definition?
>
> >
>
> >Consider;
>
> >
>
> >Impasse. A difficulty encountered in the attempted
>
> > four coloring of a graph.
>
> >
>
> >Type I " An impasse that is created by the presence of a
>
> >vertex adjacent to four other vertices, each of which has an
>
> >assigned color that is different from the assigned color any
>
> > of the three other vertices".
>
> >
>
> >Type II "All other impasses."
>
>
>
> No, I don't view that as an acceptable definition.
>
>
>
> It appears your concept of a forced 5-set in a graph G is a
>
> set of 5 vertices, S = {a,b,c,d,e} say, such that
>
>
>
> (1) Not all vertices of S are adjacent.
>
>
>
> (2) One of the vertices of S, e say, is adjacent to the other 4.
>
>
>
> (3) Vertices a,b,c,d have already somehow been forced to have
>
> 4 distinct colors.
>
>
>
> My objection is to property (3). It's not clear what it means.
>
>
>
> quasi

I hope I finally understand. Tho vertices in 3 are not
"forced". Their colors are arbitrarily assigned by the creator of the graph.

bill

Date Subject Author
6/18/13 b92057@yahoo.com
6/18/13 Tucsondrew@me.com
6/18/13 Tucsondrew@me.com
6/18/13 quasi
6/18/13 Tucsondrew@me.com
6/18/13 quasi
6/19/13 trj
6/20/13 b92057@yahoo.com
6/20/13 quasi
6/20/13 b92057@yahoo.com
6/22/13 b92057@yahoo.com
6/23/13 quasi
6/25/13 b92057@yahoo.com
6/25/13 quasi
6/25/13 b92057@yahoo.com
6/26/13 quasi
6/26/13 Brian Q. Hutchings
6/27/13 b92057@yahoo.com
6/27/13 quasi
6/27/13 b92057@yahoo.com
6/27/13 quasi
6/27/13 quasi
6/28/13 b92057@yahoo.com
6/28/13 quasi
6/28/13 b92057@yahoo.com
6/29/13 quasi
7/1/13 b92057@yahoo.com
7/2/13 quasi
6/19/13 b92057@yahoo.com
6/19/13 quasi
6/20/13 b92057@yahoo.com
6/20/13 Tucsondrew@me.com
6/21/13 quasi
6/21/13 quasi
6/22/13 b92057@yahoo.com
6/23/13 quasi
6/19/13 b92057@yahoo.com
6/20/13 quasi
6/20/13 quasi
6/20/13 Butch Malahide
6/20/13 Butch Malahide
6/19/13 b92057@yahoo.com
6/20/13 b92057@yahoo.com